Reduce to lowest terms: $ \dfrac{2}{5} \div - \dfrac{4}{5} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{4}{5}$ is $- \dfrac{5}{4}$ Therefore: $ \dfrac{2}{5} \div - \dfrac{4}{5} = \dfrac{2}{5} \times - \dfrac{5}{4} $ $ \phantom{ \dfrac{2}{5} \times - \dfrac{5}{4}} = \dfrac{2 \times -5}{5 \times 4} $ $ \phantom{ \dfrac{2}{5} \times - \dfrac{5}{4}} = \dfrac{-10}{20} $ The numerator and denominator have a common divisor of $10$, so we can simplify: $ \dfrac{-10}{20} = \dfrac{-10 \div 10}{20 \div 10} = -\dfrac{1}{2} $